The salinity in estuaries continuously adapts to varying forcing for example, by discharge and tidal conditions. The changes in salinity lag behind the changes in forcing. Previous work has mostly related this delay to the adjustment time, which depends on an average background state of the estuary. Payo-Payo et al. (2022), https://doi.org/10.1029/2021jc017523 showed that adjustment time however cannot explain the actually observed delays for a realistic salinity and forcing signal. Inspired by this, this study aims to develop relations between delay time and forcing variations and background state of the estuary. To this end, I first propose a definition of the actual delay of salinity based on wavelet analysis, applicable to observed or modeled salinity signals. To compare delay to estuarine parameters, I use a linear 1D model, but qualitative results carry over to the general case. Using model experiments with harmonic and peaked variations in the forcing, the delay time depends not only on the adjustment time, but also on the timescale of the forcing variation. Even for forcing timescales that are up to a factor 100 longer than the adjustment time, both forcing timescale and adjustment time are important for the delay. A second novel finding is that the delay depends strongly on the position along the estuary where the delay is observed. As verification, model experiments with realistically varying forcing were done, roughly inspired by the Modaomen Estuary (China). Although delay times showed a complicated and scattered dependency on model variables in this case, the above qualitative conclusions were confirmed.

Estuaries often show regions in which Chlorophyll-a (Chl-a) accumulates. The location and magnitude corresponding to such accumulation result from a complex interplay between processes such as river flushing, salinity, nutrients, grazing on phytoplankton, and the light climate in the water column. An example is the multi-annual evolution of the estuary-scale Chl-a distribution in the Scheldt estuary (Belgium/Netherlands) in spring. From 2004–2007, we observed a limited spring bloom in the brackish region (km 60–90 from the mouth, salinity ∼ 1–10 ppt). This bloom intensified in 2008–2014 and disappeared after 2015. This multi-annual evolution of Chl-a has been hypothesized to be linked to simultaneous multi-annual trends in the suspended particulate matter (SPM) distribution in summer and winter between 1995–2015 and the improvement of the water quality (e.g., reduction of ammonium), which affects grazing on phytoplankton by zooplankton. However, this hypothesis has not been systematically investigated. In this contribution, we apply a modeling approach in which observations are the core. We first analyze multi-annual in situ observations covering the full estuary. These observations include the SPM concentration, zooplankton abundance, and other variables affecting the Chl-a concentration. They show a multi-annual estuary-scale evolution not only in the SPM distribution but also in zooplankton abundance, freshwater discharge, and phytoplankon photosynthetic characteristics. Next, we apply a model approach that consists of an extensive sensitivity study and four model scenarios that are supported by these observations to constrain the processes and corresponding parameter variability that may have caused the observed change in Chl-a. Our results suggest that a change in SPM alone cannot explain the Chl-a observations. Instead, a multi-annual change in mortality rate, which we can attribute to both grazing by zooplankton and phytoplankton community (i.e., mortality dependence on salinity), may explain the multi-annual estuary-scale evolution of Chl-a in spring. Different model parameter choices may thus lead to similar model results (equifinality). Our results highlight that insight into the zooplankton dynamics and phytoplankton community characteristics is essential to understand the phytoplankton (cf. Chl-a) dynamics in the Scheldt estuary and that additional data regarding mortality and grazing rates is required to further constrain the model parameters.

An estuarine turbidity maximum (ETM) results from various subtidal sediment transport mechanisms related to, e.g., river, tides, and density gradients, which have been extensively analysed in single-channel estuaries. However, ETMs have also been found in estuaries composed of multiple interconnected tidal channels, where the water and suspended fine sediments are exchanged at the junctions with possible occurrence of sediment overspill. The overall aim of this study is to understand the processes that determine the ETM dynamics in such channel networks. Specifically, focusing on the ETMs formation due to sediment transport by river flow and density-driven flow, the dependence of ETM locations in an idealised three-channel network on fluvial sediment input and the local deepening and narrowing of a seaward channel is investigated. It is found that the ETM dynamics in channels of a network is coupled, and hence, changes in one channel affect the ETM pattern in all channels. Sensitivity results show that, keeping river discharge fixed, a larger fluvial sediment input leads to the upstream shift of ETMs and an increase in the overall sediment concentration. Both deepening or narrowing of a seaward channel may influence the ETMs in the entire network. Furthermore, the effect of either deepening or narrowing of a seaward channel on the ETM locations in the network depends on the system geometry and the dominant hydrodynamic conditions. Therefore, the response of the ETM location to local geometric changes is explained by analysing the dominant sediment transport mechanisms. In addition to the convergence of sediment transport mechanisms in single-estuarine channels, ETM dynamics in networks is found to be strongly affected by net exchange of sediment between the branches of a network. We find that considering the sensitivity of net sediment transport to geometric changes is needed to understand the changing ETM dynamics observed in a real estuarine network.

Many estuaries exhibit seasonality in the estuary-scale distribution of suspended particulate matter (SPM). This SPM distribution depends on various factors, including freshwater discharge, salinity intrusion, erodibility, and the ability of cohesive SPM to flocculate into larger aggregates. Various authors indicate that biotic factors, such as the presence of algae and their excretion of sticky transparent exopolymer particles (TEP), affect the flocculation and erosion processes. Consequently, seasonality in these biotic factors may play a role in the observed seasonality in SPM. Whereas the impact of abiotic factors on seasonality in SPM is well studied, the relative contribution of biotically induced seasonality is largely unknown. In this study, we employ two approaches to assess the aggregated importance of biotically induced seasonality in flocculation and erosion on seasonality in SPM in the Scheldt estuary. In the first approach, we focus on seasonality of in situ observations in the Scheldt estuary of turbidity, floc size, Chlorophyll-a, and TEP, showing that the abiotic parameters show seasonality, while seasonality in TEP is ambiguous. The second approach concerns a reverse engineering method to calibrate biotically affected parameters of a coupled sediment transport-flocculation model to turbidity observations, allowing us to compare the modeled SPM concentrations to the observations. Driven by seasonality in freshwater discharge, the model captures the observed seasonality in SPM without requiring biotically induced seasonality in flocculation and erosion, which is supported by the absence of seasonality in TEP.

We investigate the hypothesis by Winterwerp and Wang (Ocean Dyn 63:1279–1292, 2013) that channel deepening in the Scheldt River Estuary could lead to a large increase in suspended sediment concentrations, with subsequent severe consequences to primary production and navigation. To this end, we use an idealised model to investigate the long-term development of the sediment concentration under the uncertainty of future changes in model parameter values and channel deepening. The water motion is calibrated to recent conditions after which the sediment concentration is validated against long-term observations and is subsequently tested for a wide range of parameter settings and deepening scenarios. We also investigate the effect of anthropogenic dumping of dredged sediments in the estuary on the sediment concentration. Deepening the channel, but keeping all other model parameters the same, we find lower long-term average sediment concentrations in most of the estuary. Thereby, our results suggest that deepening in the Scheldt alone cannot lead to high sediment concentrations, and we suggest to reject the investigated hypothesis. Further study of uncertain model parameters reveals that an increase of the erosion parameter by an order of magnitude allows for the development of high concentrations of several tens of grams per liter near the bed in narrow turbidity zones. It is unknown whether such an increase of the erosion parameter can happen in the future, which stresses the importance of further research into the factors that can lead to a change of this parameter.

Phytoplankton biomass in estuaries is controlled by complex biological and chemical processes that control growth and mortality, and physical processes that control transport and dilution. The effects of these processes on phytoplankton blooms were systematically analyzed, focusing on identifying the dominant controlling factors out of river-induced flushing, tidal dispersion, nutrient limitation, and light limitation. To capture the physical processes related to flow and sediment dynamics, we used the idealized width-averaged iFlow model. The model was extended with a nutrient-phytoplankton module to capture the essential biological-chemical processes. The model was applied to the Delaware River Estuary for the productive months of March to November. Model results were compared with field observations. It was found that phytoplankton blooms cannot form in the lower bay due to tidal dispersion, as water from the estuary and coastal ocean mix in early spring, and due to local effects of nitrogen limitation in summer. In the middle to upper bay, sediment-induced deterioration of the light climate limits the growth but allows for blooms in the mid bay, while no blooms can form in the turbidity maximum zone in the upper estuary. Further upstream in the tidal river, the effects of river-induced flushing dominate in early spring and prevent bloom formation. In the summer and fall, lower river discharges and higher growth rates at higher temperatures allow blooms to form and persist. Analysis of the connectivity between mid bay and tidal river blooms showed that coastal ocean phytoplankton may contribute to mid bay blooms, but do not penetrate beyond the turbidity maximum zone.

The iFlow modelling framework is a width-averaged model for the systematic analysis of the water motion and sediment transport processes in estuaries and tidal rivers. The distinctive solution method, a mathematical perturbation method, used in the model allows for identification of the effect of individual physical processes on the water motion and sediment transport and study of the sensitivity of these processes to model parameters. This distinction between processes provides a unique tool for interpreting and explaining hydrodynamic interactions and sediment trapping. iFlow also includes a large number of options to configure the model geometry and multiple choices of turbulence and salinity models. Additionally, the model contains auxiliary components, including one that facilitates easy and fast sensitivity studies. iFlow has a modular structure, which makes it easy to include, exclude or change individual model components, called modules. Depending on the required functionality for the application at hand, modules can be selected to construct anything from very simple quasi-linear models to rather complex models involving multiple non-linear interactions. This way, the model complexity can be adjusted to the application. Once the modules containing the required functionality are selected, the underlying model structure automatically ensures modules are called in the correct order. The model inserts iteration loops over groups of modules that are mutually dependent. iFlow also ensures a smooth coupling of modules using analytical and numerical solution methods. This way the model combines the speed and accuracy of analytical solutions with the versatility of numerical solution methods. In this paper we present the modular structure, solution method and two examples of the use of iFlow. In the examples we present two case studies, of the Yangtze and Scheldt rivers, demonstrating how iFlow facilitates the analysis of model results, the understanding of the underlying physics and the testing of parameter sensitivity. A comparison of the model results to measurements shows a good qualitative agreement. iFlow is written in Python and is available as open source code under the LGPL license.